Touch Sensitive Device

ABSTRACT

An apparatus including a touch sensitive screen having a face adapted to receive a user&#39;s hand-writing via a hand-held stylus. The screen includes means exciting the screen to vibrate so as to transmit the vibration to the stylus to simulate the sensation of a writing implement writing on paper as the stylus is moved over the face of the screen. The apparatus may include means for period modulating the electrical signal applied to the exciting means and means for amplitude modulating the electrical signal. The apparatus may include means for sensing the velocity of movement of the stylus over the screen face and means for modulating the vibration according to the sensed velocity.

TECHNICAL FIELD

The invention relates to touch sensitive devices including touchsensitive screens or panels, in particular panels for use with a stylusor other writing instrument.

BACKGROUND ART

U.S. Pat. No. 4,885,565, U.S. Pat. No. 5,638,060, U.S. Pat. No.5,977,867, US2002/0075135 describe touch-operated apparatus havingtactile feedback for a user when touched. In U.S. Pat. No. 4,885,565 anactuator is provided for imparting motion to the CRT when the actuatoris energised to provide tactile feedback. In U.S. Pat. No. 5,638,060, avoltage is applied to a piezo-electric element which form a switch tovibrate the element to apply a reaction force to a user's finger. InU.S. Pat. No. 5,977,867, a tactile feedback unit generates a mechanicalvibration sensed by the user when the touch screen is touched with afinger or a pointer. The amplitude, vibration frequency and pulse lengthof the mechanical vibration are controlled, with the pulse width beinglong enough to be felt but short enough to terminate before the next keytouch. US2002/0075135 describes the use of a second transducer toprovide a pulse in the form of transient spike to simulate a buttonclick.

In each of the prior art documents described above, tactile feedback isprovided in response to a discrete touch, of a user's finger or pointer.However, it is recognised by the applicant that tactile feedback mayalso be useful for continuous movements across the touch screen.

DISCLOSURE OF INVENTION

According to the invention, there is provided a method of simulating thesensation of a writing implement writing on paper when using a hand-heldstylus to write on a touch-sensitive screen, comprising arranging thescreen to vibrate when contacted by the stylus to provide userfeed-back.

Paper comprises a fibre mat in a binder with individual fibres having arandom orientation resulting in a rough surface having local variationsin the coefficient of friction (sliding or static) on the level tracedby the small contact patch between the tip of a pencil and the papersurface. The motion of a pencil over the surface may be described asstick-slip style motion. A similar effect is felt when writing withother writing instruments, such fibre tip pen. For other types ofwriting instruments, variations on the effect may be felt. For examplefor a fountain pen this may be scratchy if a bad nib but have asmoothish, water lubricated glide if good. The type of paper also has aneffect and often fountain pen users are selective about finding paperwith the right nib feel and which takes ink at the right rate withoutbleeding. For biros, there is a viscous smooth friction sliding but thepaper does have some underlying fibrous texture.

In contrast, when writing with a stylus or pointer on a polymer or glasscover of a touch sensitive panel or surface, this slip-stick motion islost. The slip stick behaviour of pencil on paper is a key element ofthe writing sensation. Writing to touch sensitive screens with a stylushas improved sensation, appeal and user satisfaction when there is asimulation of the pencil on paper writing characteristic.

The screen may be vibrated by applying a signal comprising multiplepulses or a stream of pulses.

The method may comprise sensing the velocity of movement of the stylusover the screen face, for example, by using a sensor. The screen may bearranged to vibrate according to the sensed velocity. Thus for a signalhaving multiple pulses, the signal may have a mean pulse rate comparableto that of the sensed velocity.

The method may comprise arranging for the vibration to simulate the dragof writing implement moving over paper by period modulating thevibration, for example for a signal having multiple pulses by changingthe spacing in time between pulses, i.e. by changing the pulse rate. Thespacing may be randomised whereby the random spacing of the paper fibresis simulated. The spacing of the pulses may in the range of ⅕ to ⅘ oftwice the mean inter-fibre spacing.

The vibration may simulate the axial reciprocating movement of writingimplement moving over paper by amplitude modulating the vibration. Theamplitude may be randomised whereby the random height of the paperfibres is simulated. The amplitude may be defined by the scale factorwhich is the tactile equivalent of the volume control in audio. Thescale factor may adjusted by the user to give a suitable level ofstimulation. The amplitude may be in the range of ⅜ to ⅞ of the scalefactor.

Two connected random sequences may thus be applied to generate thevibration, a first sequence to account for inter-fibre spacing and asecond to account for the height of the fibres. Together the randomsequences may simulate a synthetic paper structure for the touch screen.

A pencil writing on paper may also have its own resonances whichcontribute to the feel of the writing sensation. Accordingly, the stylusmay be configured so that it is excited into beam resonance in responseto vibration of the screen whereby the vibration simulates resonance ofwriting implement moving over paper.

The screen may be excited to produce a sound effect simulating that ofwriting implement writing on paper.

The vibration may include any type of vibration, including bending wavevibration, more specifically resonant bending wave vibration.

According to another aspect of the invention, there is providedapparatus comprising a touch sensitive screen having a face adapted toreceive and record a user's hand-writing via a hand-held stylus, whereinthe screen comprises a vibration exciter exciting the screen to vibrateso as to transmit the vibration to the stylus to simulate the sensationof a writing implement writing on paper as the stylus is moved over theface of the screen.

The vibration exciter may comprise means for applying a bending wavevibration to the screen face. The vibration exciter may beelectro-mechanical and may comprise signal generating means for applyingan electrical signal to the vibration exciter to cause the exciter tovibrate the screen.

The signal generating means may comprise means generating a signalcomprising multiple pulses, e.g. phase locked loop module generating astream of pulses having a mean pulse rate. The apparatus may comprisemeans for sensing the velocity of movement of the stylus over the screenface. The means for modulating the vibration may be configured tomodulate the vibration according to the sensed velocity, for example,the means generating the pulsed signed may be configured to adjust themean pulse rate to match the sensed velocity.

The apparatus may comprise means for period modulating and/or means foramplitude modulating the electrical signal. The period and/or amplitudemodulation may be random and may be applied by a jitter module.

The signal generating means may generate a signal to cause the screen toradiate an acoustic component simulating that of a writing implementwriting on paper, the acoustic signal being modulated by the velocitysensing means.

The signal generating means may further comprise a filter to reducehigh-frequency content. In this way, a realistic feel may be providedwith as little noise as possible.

The vibration exciter may be a moving coil transducer or a piezoelectricbending transducer, for example one comprising a resonant element asdescribed e.g. in WO01/54450, incorporated herein by reference. Theexciter may be inertial

The touch screen may be a panel-form member which is a bending wavedevice, for example, a resonant bending wave device. The touch screenmay also be a loudspeaker wherein a second vibration exciter excitesvibration which produces an acoustic output. For example, the touchscreen may be a resonant bending wave mode loudspeaker as described inInternational Patent Application WO97/09842 which is incorporated byreference.

Contact by the stylus on the screen may be detected and/or tracked asdescribed in International patent applications WO 01/48684, WO 03/005292and/or WO 04/053781 to the present applicant. These International patentapplications are hereincorporated by reference. Alternatively, otherknown methods may be used to receive and record or sense such contacts.

The invention further provides processor control code to implement theabove-described methods, in particular on a data carrier such as a disk,CD- or DVD-ROM, programmed memory such as read-only memory (Firmware),or on a data carrier such as an optical or electrical signal carrier.Code (and/or data) to implement embodiments of the invention maycomprise source, object or executable code in a conventional programminglanguage (interpreted or compiled) such as C, or assembly code, code forsetting up or controlling an ASIC (Application Specific IntegratedCircuit) or FPGA (Field Programmable Gate Array), or code for a hardwaredescription language such as Verilog (Trade Mark) or VHDL (Very highspeed integrated circuit Hardware Description Language). As the skilledperson will appreciate such code and/or data may be distributed betweena plurality of coupled components in communication with one another.

BRIEF DESCRIPTION OF DRAWINGS

The invention is diagrammatically illustrated, by way of example, in theaccompanying drawings in which:—

FIG. 1 a is a plan view of a touch sensitive screen;

FIG. 1 b is a block diagram of the system for use with the touchsensitive screen of FIG. 1 a;

FIG. 2 is a flow chart showing the interaction of the various componentsin the system of FIG. 1 b;

FIG. 3 a shows the impulse responses of four signals which may begenerated by the system of FIG. 1 b;

FIG. 3 b shows the smoothed frequency spectra of the signals of FIG. 3a;

FIG. 4 shows a 2-D model of pencil on paper;

FIG. 5 a shows the trace history of the reactions at a hand holding thepencil in FIG. 4 during FE simulation;

FIG. 5 b shows the trace history of the pencil tip in FIG. 4 during FEsimulation;

FIG. 6 a plots the surface fibre distribution in time (tc) and amplitude(h) for a randomised surface structure;

FIG. 6 b is a smoothed version of the sampling spectrum for thestructure of FIG. 6 a;

FIG. 6 c shows the smoothed acceleration and force spectrum for thestructure of FIG. 6 a measured at 44.1 kHz;

FIG. 7 a plots the modified haptic click signal against time;

FIG. 7 b plots the spectrum of the modified haptic signal of FIG. 7 aand the target spectrum;

FIG. 8 a plots an alternative modified haptic click signal against time;

FIG. 8 b plots the spectrum of the modified haptic signal of FIG. 8 aand the target spectrum;

FIG. 9 a plots the scaled variation in amplitude over time for fourtypes of signals, and

FIG. 9 b plots the frequency spectra of the generated randomised tactilesignals corresponding to each of the impulse signals of FIG. 9 a.

DESCRIPTION OF EMBODIMENTS

FIG. 1 a shows a touch sensitive device 10 comprising a touch sensitivescreen 12 on which a stylus 18 or pencil or similar writing instrumentis being used to write text 20. One or more sensors 17 are used todetect a touch or movement of the stylus on the screen and an exciter 16is provided to generate a signal within the screen. The slip stickbehaviour of pencil on paper is a key element of the writing sensation.Writing to touch sensitive surfaces with a stylus has improvedsensation, appeal and user satisfaction when there is simulation of thepencil on paper writing characteristic.

FIG. 1 b shows how the touch sensitive device 10 may be adapted to usehaptic methods and mechanical feedback technology to create such asimulation. The writing surface is mechanically energised under thepre-programmed control of the writing input from the stylus to simulatethe feel of pencil on paper. As explained in more detail below, a modelincluding the inherent mechanical behaviour of a pencil may beincorporated into the system but this would not be recognised orunderstood by a user who simply feels the result of the simulation.

As shown in FIG. 1 b, the touch sensitive screen 12 is connected to asensor 16 which detects the nature of the contact from the stylus. Thesensor is connected to PLL (phase locked loop) 24 which is one of thekey elements used to generate the algorithm to generate the desiredsensation of pencil on paper. The elements of the algorithm may beimplemented in hardware or software. The individual elements have thefollowing description:

Short Element description Function PLL module 24 Phase-Locked Provides astream of pulses having a mean impulse Loop rate locked to the speed ofwriting as determined by software from the touch screen. Jitter module26 Pulse Randomly modifies the regular pulses into pulses randomiser ofvarying amplitude and separation according to statistical rules Fs 32Audio sample Generates clock for audio samples (texture) rate ImpulseFIR filter Impulse response that is triggered by the jittered generator28 pulses Filter 30 Optional post- Reduces high-frequency content tomake quieter filter

The PLL and Jitter blocks 24,26 run at the relatively slow rate set bythe resulting pulse train. This should be below 150 Hz average rate, butthe resolution of the jitter should be closer to the audio rate. Theaudio rate, Fs, is set as appropriate for the signal bandwidth required,but will almost certainly be no more than 11025 Hz (i.e. ¼ of thestandard CD audio rate). Where multiple audio channels are used, thesesignals may be multiplexed in a single channel. Thus where four audiochannels are used, and instead of having four channels at 11025 Hz, itwould be possible to have one audio channel of 44100 Hz, which would betime-domain multiplexed (TDM) into four haptic channels. The output fromthe filter 30 is sent to an exciter 17 which generates the signal in thescreen to simulate the desired feel.

FIG. 2 is a flow chart showing the steps implemented by each block inthe system. The sensor, which may be implemented as software on thetouch sensitive device, is monitoring the touch sensitive screen. When a“touch” is detected as at step S10, it requests a “haptic click” (stepS12) from the signal generator or impulse generator 28 and the impulsegenerator generates a pulse which provides a “click” sensation at stepS28. Screen surfaces are generally softish and quite well damped. Thusthe stylus impact is rather quiet. The “click” may or may not provide anaudible feedback depending on the proposed use for the touch screen.When a “drag” is detected as at step S14, the sensor monitors thechanges in position and calculates the drag rate, or velocity as at stepS16. This velocity data is then fed to the PLL module 24 which producesa stream of pulses. When the stylus lifts, the sensor detects no touchas at step S30 and sends instructions to the PLL to stop (step S32). Atstep S34, the PLL stops generating any commands.

The pulses used for the haptic click sensation may be the same as thepulses which form the basis of the writing simulation but are notnecessarily the same. For example, in the suggested implementationbelow, they are different. The spectra of the different signals are allchosen to match the sensitivity of the finger-tips to vibration.

The function of the PLL module 24 is described as follows. At step S18,on receipt of velocity information from the sensor, the PLL moduleprovides a steady stream of pulses which act as start commands to theJitter module (step S20). The PLL module measures the mean error betweenthe rate of this stream (the actual rate) and the incoming velocityestimates (the target rate) and adjusts the actual rate to match thetarget. The PLL module should provide memory and some filtering, so thatin the presence of noisy or missing estimates there is still a regularoutput. In summary,

Inputs: Start/Stop, Velocity (target rate)Outputs: Pulses at target rateFunction: Measure mean error between target and actual rates, and adjustappropriately.Notes: Target pulse frequency=drag velocity/inter-fibre spacing

The function of the Jitter module 26, which provides the synthetic paperstructure to the texture, is described as follows. At step S20, theJitter module 26 assigns a random amplitude to the pulse, and then atstep S22, delays the pulse for a random duration before passing it on tothe signal or impulse generator 28 at step S24. The statistics of theamplitude distribution are unconstrained by the pulse rate, but theaverage delay should be ½ the inter-pulse spacing, which means that someknowledge of the pulse rate is required. In summary,

Inputs: Synchronisation (start), mean rateOutput: Amplitude, delayed synchFunction: Effectively, a programmable mono-stable with additional output

The Beta distribution may be used for the random signals. This sets thecorrect mean and variance for both jitter and amplitude data. The valueschosen “by inspection” seem close to optimal—other values tested produceless realistic sensations. Generating Beta statistics by software orhardware may be difficult, so pragmatically it is suggested to use asimple uniform distribution (i.e. rectangular distribution) of the samemean and variance. The rectangular distribution is by far the simplestto generate and is as good as, or almost as good as the most complicatedversion

The standard way of generating a uniform distribution of samples bysoftware or hardware is the PRBS, or pseudo-random bit sequence. This isproduced by a shift-register with feed-back occurring on certain bitpatterns, or masks. The choice of mask affects the repeat length of thesequence and the “whiteness” of the noise.

A standard method for generating a specified statistical distributionfrom the uniform distribution is the so-called “Inverse transformsampling” method (see. It maps noise samples from a uniform distributionon (0, 1] into samples having the specified statistical distribution.For this method, it is necessary to know the inverse of the cumulativedensity function. A simple example follows;

Assume a target uniform distribution on (a, b]; the probability densityfunction (PDF) is

${{PDF}(x)} = \{ \begin{matrix}{1/( {b - a} )} & {{{{if}\mspace{14mu} a} < x<=b};} \\0 & {otherwise}\end{matrix} $

The cumulative density function (CDF) is obtained by integrating thePDF. The inverse CDF is a function that inverts the CDF, i.e.CDF⁻¹(CDF(x))=x. From the PDF, it is also possible to calculate the meanand standard deviation. Fixing any two different statistical propertiesallows a and b to be determined.

Unfortunately, the inverse CDF in closed form is not known for the Betadistribution, hence this method does not help. However, we may look atsimilar distributions which do have a known inverse CDF, and use theseinstead. The simplest approximation is the triangular distribution, socalled because its PDF is in the shape of a triangle. In its mostgeneral form, it is controlled by three variables; a, b and c. In asimplified form, a=0, b=1 and 0<=c<=1 and

${{PDF}(x)} = \{ \begin{matrix}{2\frac{x - a}{( {b - a} )( {c - a} )}} & {{{{if}\mspace{14mu} a} < x<=c};} \\{2\frac{b - x}{( {b - a} )( {b - c} )}} & {{{{if}\mspace{14mu} c} < x<=b};} \\0 & {otherwise}\end{matrix} $

The closest approximation to the Beta distribution is the Kumaraswamydistribution. It is controlled by two variables, a and b (real andpositive), and is bound on [0,1] with

${{PDF}(x)} = \{ \begin{matrix}{{abx}^{a - 1}( {1 - x^{a}} )}^{b - 1} & {{{{if}\mspace{14mu} 0} < x<=1};} \\0 & {otherwise}\end{matrix} $

Each of the three distributions highlighted above may be used togenerate randomness to simulate texture. Each sample requires two setsof random data—the spacing and the amplitude. In principle, these twosets could be completely independent, but testing suggests that theyshould be generated from the same uniform distribution. (This does makesome sense, as a long gap will be associated with a large amplitude anda small gap with a small amplitude, thus making the signal energy moreuniform).

Distribution Parameters for spacing Parameters for amplitude Kumaraswamya = 3, b = 5 a = 5, b = 3 Triangular [0, 1] a = 0, b = 1, c = 0.5 a = 0,b = 1, c = 0.75 Rectangular a = 0.207, b = 0.793 a = 0.375, b = 0.875

Plotting the PDF together with the spectra for each distributionsuggests that the “odd man out” is the triangular distribution. The maindifferences are in the 1-5 Hz range, and to a lesser extent at the 50 Hzmean repetition rate. Allowing the triangular distribution to cover thefull range is not best. The rectangular distribution is as good as, oralmost as good as the most complicated version (Kumaraswamy) and thus isthe most logical choice since it is by far the simplest to generate.

The function of the impulse generator 28, which provides spectralproperties of the texture, is described as follows. On receipt of asignal from the jitter module 26, the impulse generator 28 outputs asignal in the form of a stream of sample values (step S26). If anotherinput is received before the stream is complete, then a new streambegins. The amplitude of the output signal is modified according to datareceived from the jitter module 26. In summary,

Inputs: Synchronisation (start), amplitudeOutput: Sequence of haptic “audio” samplesFunction: Filter the pulse train into an analogue signal

This function may be selected from a number of mathematical models andfed appropriate (adjustable) parameters. Using these functions,arbitrary non-integer roll-off rates are possible as explained below.The impulse generator comprises a FIR (finite impulse response) filterto match the haptic signal output from the impulse generator 28 to thesensitivity of the fingers to touch. The filter may reduce thehigh-frequency content to a reasonable level.

The optional filter 30 may be provided to reduce any remaininghigh-frequency breakthrough from the impulse generator. It is envisagedthat this will be a very simple recursive, 1^(st) order stage filterwith coefficients chosen to avoid multiplication; e.g. 2̂(−n), 1-2̂(−n).If this proves insufficient, a 2^(nd) order filter could be usedinstead. The cut-off frequency would be around, say, 500 Hz-600 Hz.

FIG. 3 a shows the impulse responses of four signals from the impulsegenerator incorporating a filter, each with a cut-off at or near 300 Hz.Filters universally have integer order roll-off; for example the R-Cnetwork of electronics has a first-order response, while the L-C-Rnetwork may have a second-order response. An n-th order roll-off on abode-plot is represented by a slope of 6×n dB per octave or 20×n dB perdecade.

Many natural phenomena have “fractal” characteristics—that is, theirdimensionality is non-integer. A simple and well known example is “1/fnoise” which has a ½ order roll-off, or a 3 dB per octave slope. Inorder to produce a signal with the right “feel” and “sound”, it wasfound useful to have the ability to assign a fully variable roll-off tothe signal. That is, its level falls as frequencŷp or its power asfrequencŷ2p.

It is known from Laplace transform theory that there is a directrelationship between the impulse response and its transfer function; andin particular between their rates of decay (see e.g. Abramowitz &Stegun, “Handbook of mathematical functions”, article 29.3.7)

$ \frac{\Gamma \; (k)}{s^{k}}\Leftrightarrow t^{k - 1} $

All these transfer functions are infinite at DC, so not particularlyuseful in practice. There are, however, more useful transform pairs thatallow synthesis in either domain.

The type 1 signal shown in FIG. 3 a is unipolar and it was found that arate of approximately 2.25 to 2.5 gave the best feel/sound. Such asignal may be generated by using a cascaded first-order roll-off filterwith unity gain pass-band. Filters of this type have the transferfunction

${H(s)} = ( \frac{a}{s + a} )^{p}$

For integer p, it is easy to see how this represents a cascade of p,first-order low-pass filters. Each filter has a cut-off frequency ofωc=a radians/sec. The roll-off rate is p-th order, i.e. 6p dB/octave. Wewish to generalise this to the case when p is not an integer.

From a table of Laplace transforms, or a program that calculates themsymbolically, we find (see e.g. Abramowitz & Stegun, “Handbook ofmathematical functions”, article 29.3.11)

$ {t^{p - 1}^{- {at}}}\Leftrightarrow\frac{\Gamma (p)}{( {s + a} )^{p}} ,{{{hence}\mspace{14mu} {h(t)}} = {\frac{a^{p}}{\Gamma (p)}t^{p - 1}^{- {at}}}}$

The impulse response is unipolar, and may be considered as ageneralisation of the exponential decay.

The filter may be a classic first order filter with p=1. This should befamiliar to anyone involved in simple systems design.

${{H(s)} = \frac{a}{s + a}},{{h(t)} = {a\; ^{- {at}}}}$

Alternatively, the filter may be a half-order filter with p=½. Thisfilter would turn white noise into pink noise above the cut-off

${{H(s)} = \sqrt{\frac{a}{s + a}}},\mspace{14mu} {{h(t)} = {{\frac{1}{\Gamma ( {1/2} )}\sqrt{\frac{a}{t}}^{- {at}}} = {\sqrt{\frac{a}{\pi \; t}}^{- {at}}}}}$

Notice the symmetrical nature of this pair—in both the time and thefrequency domains, the power-law is the reciprocal square root. It isthis symmetrical nature which is at the heart of the explanation of 1/fnoise (it is a quantum-mechanical phenomenon).

The type 2 signal shown in FIG. 3 a is bipolar and it was found that arate of approximately 1.75 to 2.0 gave the best feel/sound. Such asignal may be generated by using a cascade second-order roll-off filterwith unity gain pass-band. Filters of this type have the transferfunction

${H(s)} = ( \frac{a^{2} + b^{2}}{( {s + a} )^{2} + b^{2}} )^{p}$

For integer p, it is easy to see how this represents a cascade of p,second-order low-pass filters. Each filter has a cut-off frequency ofωc=sqrt(a²+b²) radians/sec, and a Q of ωc/2a. The roll-off rate is 2p-thorder, i.e. 12p dB/octave. Again, we wish to generalise this to the casewhen p is not an integer.

From a table of Laplace transforms, or a program that calculates themsymbolically, we find (see e.g. Abramowitz & Stegun, “Handbook ofmathematical functions”, article 29.3.57 &29.2.12)

$ {({bt})^{p}^{- {at}}{J_{p}({bt})}}\Leftrightarrow{2^{p}\frac{\Gamma( {p + \frac{1}{2}} )}{b\sqrt{\pi}}( \frac{b^{2}}{( {s + a} )^{2} + b^{2}} )^{p + \frac{1}{2}}} ,$

where J_(p) is a Bessel function of order p.

hence${h(t)} = {b\frac{\sqrt{2\pi}}{\Gamma (p)}( \frac{a^{2} + b^{2}}{2b^{2}} )^{p}({bt})^{p - \frac{1}{2}}^{- {at}}{J_{p - \frac{1}{2}}({bt})}}$

The impulse response is bipolar, and may be considered as ageneralisation of the damped sinusoid.

The filter may be a classic second-order filter with p=1. This classicfilter transforms to the familiar damped sinusoid in the time domain.

${{H(s)} = \frac{a^{2} + b^{2}}{( {s + a} )^{2} + b^{2}}},{{h(t)} = {{b\sqrt{2\pi}( \frac{a^{2} + b^{2}}{2b^{2}} )({bt})^{\frac{1}{2}}^{- {at}}{J_{\frac{1}{2}}({bt})}} = {\frac{a^{2} + b^{2}}{b}^{- {at}}{\sin ({bt})}}}}$

Alternatively, the filter may be first-order filter with a Q and p=½.

${{H(s)} = \sqrt{\frac{a^{2} + b^{2}}{( {s + a} )^{2} + b^{2}}}},\mspace{14mu} {{h(t)} = {\sqrt{a^{2} + b^{2}}^{- {at}}{J_{0}({bt})}}}$

The time-domain response is simply a damped, zeroth order Besselfunction. For large t, the trigonometric approximation may be used (seee.g. Abramowitz & Stegun, “Handbook of mathematical functions”, article9.2.1), i.e.

${h(t)} \approx {\sqrt{a^{2} + b^{2}}^{- {at}}\sqrt{\frac{2}{\pi \; {bt}}}{\cos ( {{bt} - \frac{\pi}{4}} )}}$

which shows that this is essentially an amplitude modulated version ofthe ½-order filter of the half order filter described above.

Neither type 1 nor type 2 signals have the colouration in sound producedby a pencil. The type 6 signal was produced by convolving the type 1signal with a similar signal of higher frequency. In this case theconvolution has a closed form. The “Type 8” signal was produced bydirectly convolving the Type 2 signal with a similar signal of higherfrequency, but lower Q.

The spectra (i.e. sound output against frequency) of the correspondingtexture signals for a mean pulse rate of 72.6 Hz are shown in FIG. 3 b.The modified spectra diverge from the original spectra from about 800Hz, and the signals are noticeably quieter in “silent mode”.

An alternative signal (type 3) may be generated using a filter havingcascaded pairs of first-order sections with two, non-equal turningpoints. Filters of this type have the transfer function

${H(s)} = {( \frac{a}{s + a} )^{p}( \frac{b}{s + b} )^{p}}$

${h(t)} = {\frac{a^{p}b^{p}}{\Gamma (p)}\sqrt{\pi}( \frac{t}{a + b} )^{p - \frac{1}{2}}^{{- \frac{a + b}{2}}t}{I_{p - \frac{1}{2}}( {\frac{a - b}{2}t} )}}$

where I_(p) is a modified Bessel function (see e.g. Abramowitz & Stegun,“Handbook of mathematical functions”, article 29.3.50)

$\mspace{20mu} {{h(t)} \approx {\frac{a^{p}b^{p}}{\Gamma (p)}( \frac{t}{a - b} )^{p - \frac{1}{2}}\sqrt{\frac{2}{( {a - b} )t}}{P( {( {{2p} - 1} )^{2},{\frac{1}{8}\frac{2}{( {a - b} )t}}} )}^{- {bt}}}}$P(μ, x) = 1 − (μ − 1)x + (μ − 1)(μ − 9)x²/2! − (μ − 1)(μ − 9)(μ − 25)x³/3! + …

One example is a cascaded first-order filter with p=1, where

${h(t)} = {{\frac{2{ab}}{a - b}^{{- \frac{a + b}{2}}t}{\sinh( {\frac{a - b}{2}t} )}} = {\frac{ab}{a - b}( {^{- {bt}} - ^{- {at}}} )}}$

As described above, the target pulse frequency of the PLL module isequal to drag velocity/inter-fibre spacing. This equation was derived bygenerating a simple 2-D model of the paper surface and pencilinteraction to understand the fundamental process. Paper is typicallymanufactured using a “web” of cellulose fibres of 2-5 mm length and afine clay coating (particles ˜0.1 um). The resulting surface has ridgesat many distance scales, but the major ones are in the range 0.1 mm to0.5 mm, depending on the paper.

Pencils are typically manufactured from a soft-wood surround (Larch orCedar) around a “lead”. The lead is actually a ceramic formed as aco-fired mixture of graphite and clay, which is usually dipped in apolymer. The typical “sound” of a pencil is a function of the hardnessof the lead and the beam resonances of the shaft. A typical series ofmodes might be, say; 350 Hz, 900 Hz, 2.0 kHz, 3.3 kHz, etc. The valueswill, of course, depend on the length of the pencil.

The mechanism, then, may be described as the stick-slip motion of thepencil over the rough paper surface, with the sound being modified bythe resonances of the pencil.

FIG. 4 shows the simple 2-D model of the paper surface and pencilinteraction in which the paper is modelled with semi-circular ridges ofequal height spaced at a regular 0.15 mm pitch. The pencil tip, and ashort section of the shaft are modelled explicitly, and the hand-armsystem is modelled by lumped parameters.

The simulation occurs in two phases, each lasting 1 second. In the firstphase, the pencil in lowered onto the paper surface, and a writing forceon 1 N is applied. In the second phase, the pencil is dragged at 1 mm/salong the paper surface. The resulting forces on the hand and motions ofthe pencil tip may be seen in FIG. 5 a and FIG. 5 b respectively. The“cogging” seen in both sets of traces is in part due to the discretenature of the model—the nodes. In real life, other texture details wouldbe likely to cause similar effects.

It is plain to see that the periodicity of the signal is directlyobtained from the drag rate and the inter-fibre spacing, i.e. thefrequency=drag rate/inter-fibre spacing.

The precise wave shape is set by the degree of control applied to thepencil. In this simulation, the velocity at the hand is constant, andthe tip follows appropriately. The opposite extreme would be to apply aconstant force sufficient to overcome the average dynamic friction. Inthis case, the velocity would be non-uniform.

FIG. 6 a shows a more realistic model of the paper surface. Statisticaldistributions of fibre distances and heights have been used to generatethe depicted randomised surface structure. The beta distribution waschosen to generate the model for two main reasons; it is bounded on[0,1] (unlike the boundless normal distribution), and with twoindependent parameters it is possible to control two of the mainstatistical parameters (the mean, the mode, and the variance). At thisstage, the exact parameters of the statistical distributions arecompletely arbitrary.

From the drag rate and the mean fibre separation, a cut-off frequency(fc) is calculated. A smoothed version of the spectrum generated by themodel of FIG. 5 a is seen in FIG. 5 b, where fc is seen to featurestrongly.

The sampling data is convolved with a leaky integrator. In themeasurements, the time-constant corresponded to 40 rad/s, but thismerely controls the amount of very low frequency information in theresulting signal. When the signal is played over the laptop loudspeaker,it sounds like a finger-nail being dragged over paper.

FIG. 6 c shows the force spectra for measurements obtained from a customwriting tool. The tool has interchangeable tips, and is fitted with aforce gauge and an accelerometer, both connected to a charge amplifier(ENDEVCO Model 133). Neither gauges are fully calibrated, but the forcegauge sensitivity is known to be close to 1 V/N. Data was acquired via aNI PCI-4452 data acquisition card. The spectrum of the measured signalis strongly affected by the speed of writing. The essentially low-passspectra has cut-off frequencies that are directly proportional to thespeed of writing. The bandwidth was roughly established by tracing overgraph paper and using a stop watch to be about 50-60 Hz at 1 inch/secwriting rate for normal paper. The bandwidth was different for differentsurfaces.

In the example of FIG. 6 c, the writing speed is about 2 in/s and thedata is sampled at 44.1 kHz. The force results measure the forcesapplied between the pencil tip and the shaft of the writing tool. Theacceleration results measure the resulting motion of the pencil. Fromthese measurements, it is possible to derive the effective impedance ofthe system by using the relation

Zm=F/v=j.2.π.f.F/a

where F=force, v=velocity, a=acceleration, f=frequency.

Bearing in mind that the accelerometer is uncalibrated, the effectiveimpedance is like the combination of a 0.4 kg mass and a 100 Ns/mdashpot. This is, in effect, acting as a lossy integrator with a cornerfrequency of about 40 rad/s.

As is clearly seen, the measured force spectra of FIG. 6 c correspondsto the simulated spectra of FIG. 6 b. The signal of FIG. 6 b is thenfiltered to apply boosts at frequencies corresponding to modes in apencil. The new signal spectrum is reminiscent of the accelerometerspectra seen in FIG. 6 c, which has some resonances in the accelerationtrace due to modes in the writing tool. When the signal is played overthe laptop loudspeaker, it sounds much more like a pencil being draggedover paper.

As shown in FIG. 2, if the sensor detects a touch, a “click” signal isrequested. One such signal is a frequency and amplitude modulated cosinefunction, i.e.

${h(t)} = {\alpha \; t\; ^{1 - {\alpha \; t}}{\cos ( \frac{\omega \; {ct}}{1 + {\beta \; t}} )}}$

h(t) is the product of g(t)—the envelope function and fm(t)—a frequencymodulating function.

where g(t)=α·t·e^(1−α·t), which has a maximum value of unity at timet=1/α.,

α is a decay rate of the envelopeβ is a parameter controlling the rate of frequency modulation, andωc is the angular frequency at time t=0.

This signal may also be used as the “type 3” signal mentioned abovewhich is used to generate handwriting texture when a drag is detected.

This cosine function signal was found to be more effective than itssine-based counterpart and further improvements are investigated belowby adding a new variable φ was added to the function. This amendedfunction is then optimally fitted to the target haptic spectrum.

${h(t)} = {\alpha \; t\; ^{1 - {\alpha \; t}}{\cos ( {\frac{\omega \; {ct}}{1 + {\beta \; t}} - \varphi} )}}$

It was observed that for the best signals, the peak of the envelope att=1/α corresponds with a peak in the cosine function. In this case, wecan set φ directly. Using elementary calculus confirms that the correctvalue sets the argument of the cosine to 0 at t=1/α, thus:

${h(t)} = {\alpha \; t\; ^{1 - {\alpha \; t}}{\cos ( {\frac{\omega \; {ct}}{1 + {\beta \; t}} - \frac{\omega \; c}{\alpha + \beta}} )}}$

as before h(t) is the product of g(t)—the envelope function and fm(t)—afrequency modulating function but in this case

${{fm}(t)} = {{\cos ( {\frac{\omega \; {ct}}{1 + {\beta \; t}} - \frac{\omega \; c}{\alpha + \beta}} )}.}$

The optimal values for the three variables—α=532.5, β=83.85, ωc=3133—areslightly different from those of the original function. In both cases,the parameters are chosen to match a spectral template which shows therelative sensitivity of the finger-tips to vibration as a function ofthe vibration frequency. The aim is to put the most energy in thefrequency range at which the fingers are most sensitive.

FIG. 7 a shows the variation in time for the envelope function g(t) andthe frequency modulation function fm(t) of the signal. FIG. 7 a alsoshows how α is derived. The timing of the first non-zero point ofintersection is equivalent to 1/α. FIG. 7 b shows the target spectrum(dotted line) which gives the desired sensation to a user and the actualspectrum of the modified function detailed above. There is a good matchbetween the two spectra. Other values of the parameters, or even othersignals, may be used to achieve similar aims. The signal of FIGS. 8 aand 8 b is just such a signal—its parameter values are also chosen tomatch a target spectrum.

FIGS. 8 a and 8 b illustrate an alternative signal having its basisstarting in the frequency domain and expressed as.

h(t)=√{square root over (2α)}t exp(0.5−αt ²)cos(ωct−φ)

Where a=96505=310.7², b=2011, φ=5.181 rad=297°.

FIG. 8 a shows that the sensitivity curve (fm(t)) resembles a normaldistribution curve. It is also known that this curve (fm(t)) is its ownFourier transform, so the time domain signal should be similar. FIG. 8 aalso shows how α and ωc are calculated. α and ωc are calculated asdescribed above. As shown in FIG. 8 b, this alternative does not provideas good a fit to the target spectrum as the signal of FIG. 7 a but hasthe main advantage that the high-frequency end of its spectrum fallsfaster.

Comparing the two signals, for the same peak amplitude, the alternativesignal appears to be 25% more energy efficient. However, some testinghas shown that 15%-20% higher amplitude is needed to get the samesensation, thereby eliminating the advantage. There is lesshigh-frequency energy in the alternative signal, which may well helpwith making it more silent. In short, there is not much to choosebetween them. The alternative signal is illustrated in FIGS. 8 a and 8 bas “type 9” signal.

FIGS. 9 a and 9 b compare four signals for effectiveness as texturewaveforms. The signals are adjusted in amplitude to give the same degreeof sensation but use different amounts of power to achieve thesensation.

Integrated Type Description rms level 3 Original haptic click with phaseoptimisation of 0.251 FIGS. 7a and 7b 6 Unipolar, dual slope generalisedimpulse, from type 1 - 0.406 see FIG. 3a 8 Bipolar, dual slopegeneralised impulse, from type 2 - 0.201 see FIG. 3a 9 Alternativehaptic click of FIGS. 8a and 8b 0.237

The type 8 signal is the most energy efficient, with the new hapticclick (type 9) coming a close second. Type 6 is the least efficient.

The quicker decay of the type 9 signal, when compared to the otherwisesimilar type 3 signal, improves the feel considerably. Type 9 is thequietest in “silent mode” in the absence of additional filtering.

The small change to the existing type 3 click described in relation toFIGS. 7 a and 7 b is worth doing—it costs nothing, and makes animprovement. Whether or not it is worth changing to the alternativesignal (type 9) will depend on subjective assessment.

The signal type currently suggested (type 8) is a minor adjustment tothe type 2 signal previously chosen. It is still the most efficient,although not by much. It is worth comparing it to the new type 9 signal.

1.-15. (canceled)
 16. A method of simulating the sensation of a writingimplement writing on paper when using a hand-held stylus to write on atouch-sensitive screen, comprising arranging the screen to vibrate whencontacted by the stylus to provide user feed-back.
 17. The method ofclaim 16, further comprising sensing the velocity of movement of thestylus over the screen face and modulating the vibration according tothe sensed velocity.
 18. The method of claim 16, further comprisingapplying a bending wave to the screen to provide the vibration.
 19. Themethod of claim 16, further comprising arranging for the vibration tosimulate the drag of a writing implement moving over paper by periodmodulating the vibration.
 20. The method of claim 16, further comprisingarranging for the vibration to simulate the axial reciprocating movementof a writing implement moving over paper by amplitude modulating thevibration.
 21. The method of claim 16, further comprising arranging forthe vibration to simulate resonance of a writing implement moving overpaper by configuring the stylus so that it is excited into beamresonance in response to vibration of the screen.
 22. The method ofclaim 16, further comprising exciting the screen to produce a soundeffect simulating that of a writing implement writing on paper.
 23. Anapparatus comprising a touch sensitive screen having a face adapted toreceive a user's hand-writing via a hand-held stylus, wherein the screencomprises means exciting the screen to vibrate so as to transmit thevibration to the stylus to simulate the sensation of a writing implementwriting on paper as the stylus is moved over the face of the screen. 24.The apparatus of claim 23, wherein the vibration exciter comprises meansfor applying a bending wave vibration to the screen face.
 25. Theapparatus of claim 23, wherein the vibration exciter iselectromechanical and comprising signal generating means for applying anelectrical signal to the vibration exciter.
 26. The apparatus of claim25, further comprising means for period modulating the electricalsignal.
 27. The apparatus of claim 25, further comprising means foramplitude modulating the electrical signal.
 28. The apparatus of claim25, further comprising means for sensing the velocity of movement of thestylus over the screen face and means for modulating the vibrationaccording to the sensed velocity.
 29. The apparatus of claim 25, furthercomprising means for sensing the velocity of movement of the stylus overthe screen face and wherein the signal generating means generates asignal to cause the screen to radiate an acoustic component simulatingthat of a writing implement writing on paper, the acoustic signal beingmodulated by the velocity sensing means.
 30. A carrier carrying computerprogram code to, when running, implementing the method of claim
 16. 31.The method of claim 17, further comprising arranging for the vibrationto simulate the drag of a writing implement moving over paper by periodmodulating the vibration.
 32. The method of claim 17, further comprisingarranging for the vibration to simulate the axial reciprocating movementof a writing implement moving over paper by amplitude modulating thevibration.
 33. The method of claim 17, further comprising arranging forthe vibration to simulate resonance of a writing implement moving overpaper by configuring the stylus so that it is excited into beamresonance in response to vibration of the screen.
 34. The apparatus ofclaim 26, further comprising means for amplitude modulating theelectrical signal.
 35. The apparatus of claim 34, further comprisingmeans for sensing the velocity of movement of the stylus over the screenface and wherein the signal generating means generates a signal to causethe screen to radiate an acoustic component simulating that of a writingimplement writing on paper, the acoustic signal being modulated by thevelocity sensing means.